The Halogen Occultation Instrument (HALOE) is a solar occultation infrared radiometer for the measurement of composition and temperature of the middle atmosphere. It recorded atmospherically attenuated solar radiance in four channels between 996 and 4081 cm-1. HALOE was a payload of the Upper Atmosphere Research Satellite (UARS) and was operational from 11 October 1991 to 21 November 2005. With about 15 UARS orbits per day and one sunrise and one sunset measurement per orbit, up to about 10 800 vertical profiles of each target quantity could be measured per year. One of the target species measured by HALOE is H2O, for which an altitude resolution of 2 to 3 km is reported . In this work we use HALOE data version 19, which was discussed in and , where a small dry bias is reported for the altitude range relevant to this paper. Problems with HALOE water vapour retrievals of an earlier data version due to aerosol have been reported by but problematic cases discussed there were no longer present in the data set we used and thus seem to have been removed . During its 14-year lifetime, HALOE H2O measurements were frequently validated . No significant instrumental drifts were found by when they compared HALOE time series with those from various independent measurements.

The Michelson Interferometer for Passive Atmospheric Sounding MIPAS, is a limb emission mid-infrared Fourier transform spectrometer designed for limb-sounding of the composition and temperature of the middle atmosphere. Its spectral coverage is 685 to 2410 cm-1. MIPAS was a core instrument of the Envisat research satellite which was launched into a polar sun-synchronous orbit on 1 March 2002. The MIPAS data record covers the time from July 2002 to April 2012, with a data gap in 2004. In the first part of the mission (2002–2004) MIPAS recorded high-resolution (HR) spectra (apodized resolution 0.05 cm-1). In March 2004 operation was interrupted due to problems with the interferometer slide until in January 2005 operation was resumed, however at reduced spectral resolution (RR, 0.121 cm-1 after apodization). In turn, the shorter optical path difference associated with the reduced spectral resolution measurements allowed for a denser tangent altitude grid and along with this a better vertical resolution, which is 4.0 km in the middle stratosphere as opposed to 4.5 km for the high spectral resolution measurements. With 14.4 orbits per day and 74 (96) limb scans per orbit in HR (RR) mode, MIPAS recorded 1065 (1382) profiles per day.

The MIPAS H2O data used here were produced with a dedicated research processor developed and operated by the Institute of Meteorology and Climate Research (IMK) team in Karlsruhe, Germany, in cooperation with the Instituto de Astrofísica de Andalucía-CSIC in Granada, Spain . The MIPAS H2O retrieval and validation is reported in , and . In this paper we have used data versions V5h_H2O_20 for the HR measurements and V5r_H2O_220/221 for the RR measurements. Versions 220 and 221 are scientifically equivalent but carry different version numbers to maintain traceability of data processing details.

The MIPAS instrument stability has been assessed (Michael Kiefer, personal communication, 2015). A possible drift due to detector-aging and resulting changes of its non-linear response was estimated at approximately -0.05 ppmv decade-1. This is in agreement with, e.g. who did not find any larger relative drifts between the Water Vapor Millimeter-wave Spectrometer and various satellite-borne instruments including MIPAS.

The eruption of Mount Pinatubo on 15 June 1991 brought enormous amounts of aerosol into the stratosphere. This aerosol layer affected the radiative transfer of solar radiation through the atmosphere and led to artefacts in the HALOE analysis . Thus, HALOE data from the first 5 months have been discarded and data since March 1992 have been used.

For harmonization with respect to altitude resolution we use the method suggested by and described in detail for application to MIPAS profiles by . The better resolved HALOE profile is degraded with a representative MIPAS averaging kernel (see , for a detailed discussion of the concept of averaging kernels) to provide a HALOE H2O profile as MIPAS with its inferior altitude resolution would have seen it. Representative MIPAS averaging kernels were constructed for each latitude band of 10 degrees coverage and for each season (Fig. ). Details of the construction of representative averaging kernels are reported in . Along with this degradation, HALOE data were resampled on the MIPAS altitude grid which has a 1 km grid width in the altitude range relevant to this study.

Figure shows the combined time series both with the original HALOE data (yellow curve) and with the degraded HALOE data (black curve). It is obvious that the amplitude of the annual cycle in HALOE data is much larger than in the MIPAS data (green and red curve). The reason is roughly this: in the case of MIPAS, the unknown variable in the retrieval is not the mixing ratio of H2O but its logarithm. Thus the Jacobian of the radiative transfer model depends directly on the mixing ratio (vmr) of water vapour, even if radiative transfer is linear with respect to vmr. For larger H2O abundances the Jacobian is larger and thus the weight of the constraint term in the retrieval is smaller and the altitude resolution is better. From this follows that MIPAS resolves the hygropause better in the wet season than in the dry season. This leads to the asymmetric distortion of the annual cycle, seen when comparing the black and the yellow curve in Fig. . Application of the season-dependent MIPAS averaging kernels to HALOE data as described above leads to a HALOE time series which is almost perfectly comparable to that of MIPAS. This pronounced effect proves that the direct analysis of MIPAS H2O time series without consideration of averaging kernels is prone to false conclusions.

The MIPAS–HALOE overlap period from July 2002 to August 2005 allows for de-biasing of MIPAS with respect to HALOE. This de-biasing was performed independently for the MIPAS HR and RR data, because these two data sets rely on different processing schemes and thus could theoretically have different characteristics. By the independent de-biasing of each of the two MIPAS data sets with respect to HALOE, biases between both the MIPAS data sets are also removed implicitly. These, however, were found to be small anyway.

Three different approaches to determine the bias were tested, one relying on coincident measurements, the other relying on latitudinal mean values, and the third minimizing the root mean square difference of the MIPAS and HALOE time series during the overlap period. The third method proved to be most robust and was finally selected. The other two candidate approaches suffered from sparse statistics or sampling artefacts, respectively. De-biasing was performed separately for each 10∘ latitude bin between 80∘ N and 80∘ S and for each altitude of the MIPAS vertical grid. An example is shown in Fig.  (red curve). The merged time series used for our further analysis is represented by black and red lines. Within the overlap period a weighted average of the homogenized HALOE and MIPAS data has been used.

Besides the constant and linear term, the annual cycle and its first three overtones (wavenumbers two, three, and four waves per year) were considered. Wavenumber two represents the semi-annual oscillations, and wavenumbers two to four help to better model the annual cycle when it is not perfectly harmonic. The following proxies were considered:

The quasi-biennial oscillation (QBO) was parametrized using Singapore winds at 30 and 50 hPa, as obtained from the Institut für Meteorologie of the Freie Universität Berlin, (http://www.geo.fu-berlin.de/met/ag/strat/produkte/qbo). Between the winds at these pressure levels, there is a phase shift of approximately π2. Thus, fitting coefficients of both of these gives access to the approximate phase and amplitude of the QBO signal cf., e.g..

For the El Niño–Southern Oscillation (ENSO) signal, the Multivariate ENSO Index (MEI) (http://www.esrl.noaa.gov/psd/enso/mei/index.html) was used as a proxy. Since this data set refers to a tropical surface pressure level, a time lag was considered to make the proxy representative for the stratospheric latitudes and altitudes considered here. To estimate the time lag, temporally averaged stratospheric mean age of air data from were used.

In the fitted time series there are pronounced systematic residuals. Some of them are related to an apparent discontinuity in the water vapour abundance in 2001, the well-known millennium water vapour drop but the fits are unsatisfactory in the entire period before 2007. The residual time series appears to be dominated by a systematic harmonic feature of a period length of about 11 years. Figure  shows the fit of the time series at 17 km altitude in the latitude bin 0–10∘ S as an example.

The fit residuals obtained by the regression analysis described in the previous section resemble a harmonic with a period of about 11 years. Besides, strong H2O decreases are visible in 1994 and 2001. The period of 11 years suggests also considering the solar cycle in the regression model. Two approaches have been tried:

Approach 1: the solar cycle was modelled by a harmonic of 127 months with an overtone of 63 months cf.. Fitting of the related sine and cosine coefficients gave access to the amplitude and phase of the solar signal. Consideration of the solar term improves the fits within 60∘ S–60∘ N in 92 % of the altitude/latitude bins (Fig. ). The improvement is most pronounced at altitudes around 25 km and reaches 20–30 % in some altitude/latitude bins. The time series at 0–10∘S , 17 km altitude is shown as an example how the new regression model fits the time series (Fig. ). While both the H2O minimum in 1994 and the so-called millennium drop in 2001 are still visible in the residual data and still calls for explanation, the majority of the systematic residuals have disappeared and the general shape of the time series is nicely reproduced by the regression model. This result suggests that the solar cycle might indeed partially control lower stratospheric water vapour.

Approach 2: alternatively to the treatment with harmonics, the solar cycle has been fitted using the radio flux index at a wavelength of 10.7 cm (F10.7) as a proxy. This index, which is available via the Solar and Heliospheric Observatory (SOHO, http://sohowww.nascom.nasa.gov/sdb/ydb/indices_flux_raw/Penticton_Observed/monthly/MONTHPLT.OBS) is proportional to solar activity. Since it is not a priori clear which solar-terrestrial processes might control the H2O content of the stratosphere and where exactly they happen, and how long the processed air travels through the stratosphere before it is observed, the phase shift obtained from Approach 1 (approximation of the solar cycle effect by harmonic functions) has also been applied to the F10.7 proxy. Delayed anti-correlation (lowest water vapour for solar maximum, shifted by several months, depending on altitude and latitude) provided the best results. The improvements over the regression without the solar term are shown in Fig. . While the improvements are less pronounced in some of the bins than for Approach 1, this approach seems to be more adequate for the inner tropical lowermost stratosphere. For 95 % of the bins within 60∘ S–60∘ N the fit has been improved compared to the standard approach without solar cycle. The altitude/latitude bin at 0–10∘ S, 17 km is shown as an example (Fig. ). In this particular case, the residual due to the millennium drop is less pronounced than in the case with the regression model using the harmonic representation of the solar cycle effect, but it is still visible.

Both approaches reveal a strong relation between the water vapour abundances and the solar cycle. The correlation is phase-shifted in a sense that lowest water vapour abundances are seen a couple of years after the solar maximum (see Fig.  as an example).

The amplitudes of the solar component in the regression model are shown in Fig.  for both the harmonic (top panel) and the F10.7 (bottom panel) parametrization. While the amplitudes associated with the harmonic approach are larger, the altitude/latitude distributions of the amplitudes associated with each approach have the same structure. Largest effects are seen around the tropical tropopause region, and smallest in the southern mid-latitudinal middle stratosphere.

The propagation of the data errors through the regression model leads to uncertainties of these amplitudes of generally less than 2 % within the tropical pipe and less than 5 % outside. Fit residuals, however, are not compliant with χ2 statistics, indicating that the regression model, even with the solar term included, is less than perfect and does not fully describe the entire variation of stratospheric H2O. Analysis of the fit residuals and consideration of resulting estimates of correlated model errors suggests an uncertainty in the order of 15 to 50 % over a larger part of the altitude/latitude range, with highest and contiguous significance (15–25 % relative error of the amplitude) in the tropical tropopause range. This provides good confidence in the results.

The phase shift of the solar signal (Fig. ) is an interesting result in itself because it helps to determine where in the atmosphere the solar-terrestrial processes controlling the stratospheric H2O content might take place. The phase shift α – which, for all altitude/latitude bins, represents a delay of the negative response of water vapour to the original solar cycle – is about 40 months at about 18 km altitude and 45 to 50 months at about 22 km altitude in the inner tropics. This implies that a certain phase α which is seen at a certain time at, e.g. 18 km altitude, is observed 5 to 10 months later at 22 km altitude. We compare this with the temporally averaged mean age of stratospheric air distribution (age(ϕ,z)) by , which is a measure of the Brewer–Dobson circulation. This data set, although for a shorter period, is the only available global observational climatology of age of air. Since the age of air changes only slowly , we consider the temporal average for 2002–2010 as approximately representative for the full period. The increase of the age of air between 18 and 22 km also is 5 to 10 months, giving the following relation.

α(ϕ,z)-α(0∘,18km)≈age(ϕ,z)-age(0∘,18km) This suggests that the solar effect is not a local one but that part of the phase shift might be caused by transport processes via the upwelling branch of the Brewer–Dobson circulation of a signal generated near the tropical tropopause. Further, the fact that the phase shift is larger than the age of air in the lowermost stratosphere suggests that the effect itself must have an inherent time lag (inh.lag). It can be estimated from the difference of the phase shift of the solar signal and the age of stratospheric air, assuming that the solar perturbation is transported from the tropical tropopause region into the stratosphere by the stratospheric residual circulation: inh.lag(ϕ,z)=α(ϕ,z)-age(ϕ,z). The inherent time lags as a function of latitude and altitude are shown in Fig. . We find that for all points below the triangle defined by the points (60∘ S, 15 km), (0∘, 23 km) and (60∘ N, 15 km) the inherent time lag is almost constant and amounts to roughly 25 months (extrema are 15 and 30 months). A slight decrease of the inherent time lag with altitude, particularly in the tropical pipe, can be explained as follows. It is well-known that the mean age of stratospheric air overestimates the pure transit time of a signal and that in the tropical pipe the discrepancy between age of air and transit time increases with altitude. Thus, the correction by age of air is too large and increases with altitude.

For higher altitudes and latitudes, the phase shift shows a different behaviour. After having reached a maximum in the lower stratosphere (green/yellow belt in Fig. ), the phase shift becomes smaller again. Moreover the inherent time lag is negative and decreases further with altitude and latitude. This hints at different processes governing the solar cycle response of water vapour at higher altitudes.

Inclusion of a solar cycle by either approach discussed in Sect. 4.2 has improved the fit of the regression model to the measured H2O time series. Inclusion of the solar component has largely reduced the systematic residuals of the fit of the time series. When the F10.7 proxy was used, even the millennium drop was – coincidentally or not – modelled much better. Regardless of if a causal relation between solar activity and the lower stratospheric H2O distribution is claimed or not, any missing descriptive term in an incomplete regression model causes residuals which are aliased onto other parameters in the fit. In the case discussed here, inclusion of the solar cycle terms leads to much more negative water vapour trends and in some altitude/latitude bins even changes the sign of the trend (Fig. ). In the standard regression model stratospheric water vapour abundances increase or decrease by less than 0.2 ppmv decade-1 nearly everywhere. In particular, a contiguous increase in the lower stratosphere in the order of 0.1–0.2 ppmv decade-1 is seen. When the solar cycle is considered, stratospheric water vapour decreases everywhere, and stronger than by -0.1 ppmv decade-1 at most latitudes and altitudes. This indicates that, even if one does not believe the solar cycle effect in explanatory terms, it still is important in descriptive terms in order to avoid artefacts caused by the related systematic residuals. This means that the related systematic residuals, whatever their cause may be, can emulate artificial trend components. Systematic effects on the annual and semiannual cycles as well as QBO and ENSO amplitudes are much less pronounced.